Hyperbolic 3-manifolds as cyclic branched coverings |
| |
Authors: | M Reni B Zimmermann |
| |
Institution: | (1) Università degli Studi di Trieste, Dipartimento di Scienze Matematiche, P. le Europa, 1, I-34126 Trieste, Italy, IT |
| |
Abstract: | There is an extensive literature on the characterization of knots in the 3-sphere which have the same 3-manifold as a common
n-fold cyclic branched covering, for some integer . In the present paper, we study the following more general situation. Given two integers m and n, how are knots K
1 and K
2 related such that the m-fold cyclic branched covering of K
1 coincides with the n-fold cyclic branched covering of K
2. Or, seen from the point of view of 3-manifolds: in how many different ways can a given 3-manifold occur as a cyclic branched
covering of knots in S
3. Under certain hypotheses, we solve this problem for the basic class of hyperbolic 3-manifolds and hyperbolic knots (the
other basic class is that of Seifert fiber spaces resp. of torus and Montesinos knots for which the situation is well understood;
the general case can then be analyzed using the equivariant sphere and torus decomposition into Seifert fiber spaces and hyperbolic
manifolds).
Received: December 7, 1999; revised version: May 22, 2000 |
| |
Keywords: | , Hyperbolic knot, cyclic branched covering, hyperbolic 3-manifold, |
本文献已被 SpringerLink 等数据库收录! |
|